Using the Webapps is what you want right?
–
Uri HerreraSep 12 '12 at 17:15

2

Please clarify/refine your definition of "integrated gmail". Do you mean integration into the messaging menu, launcher panel, HUD, and dash? Or were you looking for integration into a desktop mail client, e.g. Thunderbird?
–
InsperatusSep 12 '12 at 20:11

That depends on that you mean by integrated... There are a number of applications you can install to manage your email, contacts, calendar, etc. But I'm not aware of anything natively built into the default Desktop environment (that includes Unity, Gnome or KDE).